Water wave scattering by floating flexible porous plate over variable bathymetry regions

Abstract

The study deals with the scattering of obliquely incident gravity waves by a horizontal floating flexible porous plate in the water of finite depth having a variable bottom bed. The problem when a vertical rigid wall is placed in the downstream of the plate is also considered. The problem is analyzed under the assumptions of small amplitude water wave theory and structural responses. The undulated bottom bed is finitely extended and lies beneath the floating plate regions. A coupled eigenfunction expansion - boundary element method is used for the solution purpose. Energy balance relations for wave scattering in the presence of the flexible plate and when the vertical rigid wall is placed in the downstream are derived and used to check the accuracy of the numerical results. The effect of sinusoidally varying bottom topography, plate porosity and heading angle of the incident wave on the Bragg resonance is analyzed. Moreover, various results are computed and analyzed to study the role of the wave parameters, bottom undulation and floating porous flexible plate on wave scattering. The proposed solution methodology can be easily extended to deal with wave-structure interaction problems of varied structural configurations and bottom bed.